Find the median of the given data by making a 'less than ogive'.

Marks
No. of Students
0-10
5
10-20
3
20-30
4
30-40
3
40-50
3
50-60
4
60-70
7
70-80
9
80-90
7
90-100
8

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68.5

68.0

69.0

67.5

answer is A.

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Detailed Solution

Given that,

Marks	No. of Students
0-10	5
10-20	3
20-30	4
30-40	3
40-50	3
50-60	4
60-70	7
70-80	9
80-90	7
90-100	8

Median can be explained as the middle number in a sorted order of ascending or descending in a list. Ogives are graphs that are used to determine how many numbers lie below or above a particular variable or value in data.
We will first calculate cumulative frequency for less than table.

Marks (Upper class limits)	Cumulative Frequency (C.F.)
Less than 10	5
Less than 20	5+3=8
Less than 30	8+4=12
Less than 40	12+3=15
Less than 50	15+3=18
Less than 60	18+4=22
Less than 70	22+7=29
Less than 80	29+9=38
Less than 90	38+7=45
Less than 100	45+8=53

In order to find the median of the grouped data using ogive graph, we need to calculate the value of N:

N = C . F 2 = 532 = 26.5

To calculate the median of the grouped data, take the upper-class limits of class intervals on x-axis and their respective frequencies on y-axis. Considering the point “N” w.r.t. x-axis, the value comes out to be 68.5.
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